# How do you find the exact value of #cos(u-v)# given that #sinu=5/13# and #cosv=-3/5#?

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Mar 20, 2017

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Find

#13^2 = 5^2 + a^2# #a^2 = 169 - 25 = 144# #a = 12#

So#cos u = 12/13#

Find

#(-3)^2 + b^2 = 5^2# #b^2 = 25 - 9 = 16# #b = 4#

So#sin v = 4/5#

Use the difference formula

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